Multiple choice

What is the 10th common term between the series 2 + 6 + 10 + …. and 1 + 6 + 11 + ?

  1. 180

  2. 186

  3. 196

  4. 206
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The first sequence has nth term 4n - 2, and the second has nth term 5n - 4. Their common terms satisfy 4n - 2 = 5m - 4, giving indices n = 2, 7, 12, and so on. The 10th common term is 4(47) - 2 = 186.

AI explanation

The two given series are arithmetic progressions with the same second term of 6. Their common terms will also form an arithmetic progression whose first term is 6 and common difference is the least common multiple of 4 and 5, which is 20. The formula for the nth term of this common progression is a + (n - 1)d. For the 10th common term, we calculate 6 + (10 - 1) * 20 = 6 + 180 = 186. The result is 186.

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